To breed, select the breeding cave and tap on the breed button. Then select the two dragons you want to breed and tap the Start button. Dragons that cannot be bred will be darkened and unselectable with a short message on why they are unavailable for breeding. Afterwards the dragons will be in the breeding cave for a set amount of time determined by the type of dragon randomly bred. The amount of time spent in the breeding cave can be reduced with the Breeding Speed perk. After the dragons are finished breeding you can tap on the breeding cave to place an egg in your nursery if you have an available slot. The egg will then incubate in the nursery for an amount of time determined by the type dragon. This incubation time cannot currently be lowered. After the egg is done incubating you may hatch the dragon and either place it in a habitat or the resort, or just sell the dragon. Whether you choose to sell or place the dragon you will gain experience.

The process of breeding dragons in Dragons World is inherently random, however by understanding how a particular dragon is randomly selected you can sometimes increase your chances of getting a specific dragon. Each breedable dragon in the game has a particular number associated with it called its probability factor. This factor is a number greater than 0 and less than or equal to 1. It is the indiviual factors on the rare dragons that are increased by the perk "+% Chance of Rare Dragon". So when breeding a pair of dragons with the max chance for rare dragons of +30%, a factor of 0.1 would become 0.13. (For dragons acquiring perks before April 1, 2014: this maximum could be upto +50%. Please see the Perks page for more information.)

When the game calculates the actual result it does so by first determining all possible breedable combinations based on the elements of the parents. Any dragon that shares all of its elements with either one or both of the parents is included. It then determines which of those dragons is rare and increases their probability factor appropriately. Then the sum of all the possible dragon's probability factors is determined. The game then produces a random number between 0 and this sum. The game checks to see which dragon's range of probability the number falls in with an exclusive upper bound and this determines the actual result of the breeding.

Now let's go back to the +% chance to breed rares perk. In the example above, the only rare dragon in the pot is the Predatory Dragon. Let's assume we have 30% extra chance to breed a rare, which increases the Predatory Dragon's probability factor by 30%, so from 0.1 to 0.13.

This would change the sum of all probability factors in the pot to 5.130003. To determine the chance of getting a Predatory Dragon, we would take its new probability factor and divide it by the new sum: 0.13 / 5.130003 ≈ 0.0253.

Once again, let's start with the first example, the chance to breed was 1.96%. Now to get a good quick estimate of the chance with +% chance to breed rares perk, multiply that number by the increased chance to breed rares (30% or .3) and add the result to the original chance.

1.96% x 0.3 = 0.59%
1.96% + 0.59% ≈ 2.55%

It doesn't come out as exact as the previous method, but for a quick calculation, it is a good estimate.

All opposing element dragons must be bred using at least one hybrid dragon with two or more elements. For example, to breed a Steam Dragon, you would want to use either a Fire or Water Dragon and then a hybrid dragon containing either the Fire or Water element, depending on which single-element dragon you are using.

The Breeding Index page, and it's sub-pages, shows the probabilities of breeding a certain dragon when using the best parent elements. It does not matter which parents these elements come from, as long as all the required ones are present, with no extras. Example: Fire + River and Lava + Water can produce the same offspring. Having extra elements involved in the breeding does not prevent the potential dragon from being bred, however, it does lower the probability that any particular dragon will result from the breeding due to there being more possible offspring from the breeding.

For a detailed list of breeding outcomes, with limited Perk calculations, see the Breeding Index page.